NBER WORKING PAPER SERIES
EXCLUSIONARY MINIMUM RESALE PRICE MAINTENANCE
John Asker
Heski Bar-Isaac
Working Paper 16564
http://www.nber.org/papers/w16564
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
December 2010
We thank the organizers and participants of CCP Summer Conference 2010 for providing sessions
prompting the ideas expressed in this paper. Specific thanks to Rona Bar-Isaac, Simon Board, Joyee
Deb, Robin Lee, Tom Overstreet, Larry White, and Ralph Winter for many helpful comments and
to seminar participants at UCLA and the University of Rochester. The usual caveat applies. The views
expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau
of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2010 by John Asker and Heski Bar-Isaac. All rights reserved. Short sections of text, not to exceed
two paragraphs, may be quoted without explicit permission provided that full credit, including © notice,
is given to the source.
Exclusionary Minimum Resale Price Maintenance
John Asker and Heski Bar-Isaac
NBER Working Paper No. 16564
December 2010
JEL No. D42,K21,L12,L42
ABSTRACT
An upstream manufacturer can use minimum retail price maintenance (RPM) to exclude potential
competitors. RPM lets the incumbent manufacturer transfer profits to retailers. If entry is accommodated,
upstream competition leads to fierce down- stream competition and the breakdown of RPM. Hence,
via RPM, retailers internalize the effect of accommodating entry on the incumbent’s profits. Retailers
may prefer not to accommodate entry; and, if entry requires downstream accommodation, entry can
be deterred. We investigate when an incumbent would prefer to exclude, rather than collude with,
the entrant and the effect of a retailer cartel. We also consider the effect of imperfect competition.
Empirical and policy implications are discussed.
John Asker
Stern School of Business
Department of Economics, Suite 7-79
New York University
44 West 4th Street
New York, NY 10012
and NBER
[email protected]
Heski Bar-Isaac
Stern School of Business
Department of Economics, Suite 7-73
New York University
44 West 4th Street
New York, NY 10012
[email protected]
Exclusionary Minimum Resale Price Maintenance∗
John Asker†and Heski Bar-Isaac‡
NYU Stern & NBER, and NYU Stern
November 17, 2010
Abstract
An upstream manufacturer can use minimum retail price maintenance (RPM) to
exclude potential competitors. RPM lets the incumbent manufacturer transfer profits
to retailers. If entry is accommodated, upstream competition leads to fierce downstream competition and the breakdown of RPM. Hence, via RPM, retailers internalize
the effect of accommodating entry on the incumbent’s profits. Retailers may prefer not
to accommodate entry; and, if entry requires downstream accommodation, entry can
be deterred. We investigate when an incumbent would prefer to exclude, rather than
collude with, the entrant and the effect of a retailer cartel. We also consider the effect
of imperfect competition. Empirical and policy implications are discussed.
JEL Codes: K21, L42, L12, D42
1
Introduction
A manufacturer engages in resale price maintenance (RPM) when it sets the price at
which its distributors must sell its product to consumers. Minimum RPM involves the
manufacturer setting a price floor for its distributors, whereas maximum RPM involves
the manufacturer setting a retail price ceiling. In the US, for almost one hundred years,
∗
We thank the organizers and participants of CCP Summer Conference 2010 for providing sessions
prompting the ideas expressed in this paper. Specific thanks to Rona Bar-Isaac, Simon Board, Joyee Deb,
Robin Lee, Tom Overstreet, Larry White, and Ralph Winter for many helpful comments and to seminar
participants at UCLA and the University of Rochester. The usual caveat applies.
†
Email: [email protected]
‡
Email: [email protected]
1
following the Supreme Court’s 1911 decision in Dr. Miles,1 minimum RPM was a per se
violation of Section 1 of the Sherman Act, though statutory exemptions have existed at
times (see Overstreet (1983) for a useful history and for data on the use of RPM under these
exemptions).2 The most cited concern about minimum RPM—a concern that persists to
this day—is that it constitutes a practice that facilitates retailer or manufacturer collusion,
by coordinating pricing and making monitoring easier (see Yamey (1954) and Telser (1960)
for early examples, and Shaffer (1991), Jullien and Rey (2007) and Rey and Vergé (2009)
for formal treatments).3
Largely in response to the per se status of RPM, a number of papers were written in the
latter part of the last century to explore pro-competitive justifications for RPM (prominent
examples include Telser (1960), Marvel and McCafferty (1984), Klein and Murphy (1988),
Deneckere, Marvel and Peck (1996, 1997) and Marvel (1994)). These papers suggest that
RPM can be in the interest of both manufacturers and consumers.
In 2007, the Supreme Court finally overturned the per se rule against minimum RPM
in the U.S. in the Leegin case, which decided that cases involving minimum RPM should
be decided on a “rule of reason” basis.4 That is, courts are now required to balance the
potential efficiency benefits of RPM against the potential anti-competitive harm. In reaching this decision, the court relied heavily on the pro-competitive theories of RPM that had
been developed in the economics literature. In the wake of the Leegin decision, economists
advising antitrust enforcers are now forced to provide explicit theories for competitive harm
that arise from RPM and must be able to quantify the extent of this harm.
This paper develops a model of competitive harm that arises from the exclusion of a
more efficient entrant by an incumbent manufacturer. In our framework, minimum RPM
is necessary for this to occur. Our framework, therefore, builds a foundation for pursuing
the third basis of antitrust harm raised in the Leegin decision (see Leegin at p.894)—the
potential for RPM to be used to provide margins to distributors that will likely disappear
1
Dr. Miles Medical Co. v. John D. Park and Sons, 220 U.S. 373 (1911)
A per se violation means that the party bringing the case is not required to establish in evidence that
harm to competition occurred. Instead, it is presumed by the mere existence of the conduct. Horizontal
price-fixing agreements are another example of a per se violation. Posner (2001, p.176ff) describes the
evolution of the Court’s treatment of the per se rule for RPM.
3
The extent to which RPM impacts consumer welfare varies over time and jurisdiction, often due to
changes in laws. Gammelgaard (1958) reports that in the United Kingdom over 30% of consumer goods
expenditure was affected by RPM between 1938 and 1950, and in Sweden in 1948 the same number was
between 25 and 28%. These numbers cover periods in which RPM was legal in these jurisdictions.
4
Leegin Creative Leather Products, Inc. v. PSKS, Inc., 551 U.S. 877 (2007), all pages references are to
the judgement as it appears in this reporter.
2
2
if entry occurs, resulting in exclusion.5 In the model, exclusion is naked in the sense that
minimum RPM serves no purpose other than to provide distributors with incentives to
exclude a potential entrant; that is, with no possibility of entry, there would be no reason to
employ RPM. The primary contribution of this paper is its rigorous framework for exploring
the idea of RPM as an exclusionary device. It also gives some preliminary guidance about
screens for, and empirical measures of, exclusion, which can be constructed from data using
econometric methods that are standard in empirical industrial organization.
At the heart of this paper is a familiar intuition: RPM limits downstream competition
and, so, can allow downstream retailers to earn relatively high profits. Indeed, it is precisely
these profits (and the threat of losing them) that have been used to provide a pro—
competitive theory of RPM: Klein and Murphy (1988) argue that manufacturers can use
these profits to entice retailers to provide the desired level of service. However, here, we
highlight a more harmful implication of such profits.6 If an entrant cannot establish itself
without some retailer support, then retailers will be hesitant to accommodate an entrant
since following manufacturer entry, retail competition will be more intense.7 Even if the
entrant manufacturer can offer RPM, retailers will shop among the manufacturers for better
terms that allow them to compete more intensely with other retailers.8 Seeking to prevent
the industry from evolving in this direction, which reduces the profitability of the whole
industry (and, in particular, their own profitability), retailers will not accommodate entry.
The incumbent manufacturer, by an appropriate choice of RPM, can ensure that the
industry as a whole earns the profits that a monopolized industry would earn, and, through
an appropriate choice of the wholesale price, divide these profits between itself and the retail
sector. To exclude entry, the incumbent must ensure that every retailer earns more than
a competing manufacturer entrant could offer the retailer to stock its good; however, this
may still allow the incumbent positive profits. Therefore, according to this theory, both the
retail sector and the incumbent manufacturer gain from RPM.9 This is in contrast to much
5
The first two bases for harm are RPM as a practice facilitating upstream collusion and as a practice
facilitating downstream collusion.
6
Shaffer (1991) also does this, in the context of RPM (and slotting fees) facilitating collusive outcomes
among retailers.
7
Comanor and Rey (2001) make a related point in the context of exclusive dealing.
8
A more efficient entrant cannot simply replicate the incumbent manufacturer, since he faces a competitor. Even though all retailers might prefer an RPM agreement with the entrant, there is no way that they
could commit to stick to such an agreement, absent collusion.
9
In line with this observation, Overstreet (1983, p.145ff) describes lobbying by both manufacturers and
retailers for the ‘Fair-Trade’ statutes that created exemptions from liability for RPM. These statutes lasted
from the 1930s through to the mid-1970s, depending on the state(s) involved.
3
of the policy discussion that suggests that there is less reason for antitrust concern when a
manufacturer instigates RPM. We return to consider policy implications in the conclusion.
First, we set out the theory and illustrate the central mechanism through a simple
model with homogeneous retailers. In contrast to much of the RPM literature, and in order
to highlight our mechanism, there is no possibility of pre- or post-sale service. Retailers
simply distribute the goods that they receive from the upstream manufacturer. We analyze
a single market; entry, of course, may reflect a manufacturer expanding from an existing
geographic location or adding a new product line that appeals to a new consumer segment.
In this environment, there are always equilibria in which entry is accommodated since,
if a retailer anticipates that some other retailer will accommodate the entrant, then it will
be keen to accommodate the entrant as well, and, thus, such beliefs can be self-sustaining.
Note, however, that in such equilibria, RPM agreements play no role and would not be
used. Our focus on equilibria where entry is excluded is, perhaps, further justified by the
observation that if such an exclusionary equilibrium exists, then not only would it involve
RPM, but also all retailers would prefer it to an accommodating equilibrium.10
We characterize the conditions under which an exclusionary equilibrium can be sustained in our baseline model and describe properties of such equilibria. In particular, we
highlight the welfare loss associated with exclusionary equilibria, which may be of practical
use to policy makers in quantifying harm. In addition, we discuss empirical screens useful
for assessing whether such equilibria are feasible and, if so, for determining preliminary
bounds on the scope of possible harm.11
The exclusionary equilibrium bears a resemblance to collusive equilibria. In light of this,
and prompted by some early accounts of exclusionary RPM, we then enrich the model to
incorporate the possibility of both manufacturer and retailer collusion. First, we ask when
an incumbent might prefer to exclude an entrant, rather than accommodating and then
colluding with it. If the collusive equilibrium does not allow explicit side-payments, then
an incumbent will prefer to exclude when the difference in marginal costs of incumbent
10
Inasmuch as both exclusionary and non-exclusionary equilibria exist, exclusion may require coordination (if only in beliefs over the equilibrium being chosen) among the downstream retailers. As we
discuss below, sometimes this has been achieved through explicit downstream coordination via, for instance,
trade associations.
11
Empirical work on RPM is limited. All recent studies attempt to test different theories of RPM.
Ippolito and Overstreet (1996) and Ornstein and Hassens (1987) conduct industry case studies, Ippolito
(1991) studies RPM litigation, while Gilligan (1986) and Hersch (1994) conduct stockmarket event studies.
Earlier empirical work is extensively surveyed in Overstreet (1983). The evidence in support of collusive
theories is mixed.
4
and entrant is large, and the fixed cost is large. The large fixed cost means that exclusion
involves comparatively small transfers to retailers. However, after entry has occurred and
the fixed cost of entry is sunk, colluding with a much more efficient producer can be supported only if the more efficient producer gets a large share of the market. Hence, exclusion
can be more profitable than collusion when the fixed cost of entry is large and marginal
cost differences are significant. Moreover, exclusion can deter several potential entrants,
whereas colluding with several entrants becomes ever less appealing. We then consider the
effect of collusion among retailers. While one might suppose that a retailer cartel should
maximize retailers’ profits and so lead to the entry of an efficient manufacturer, a retailer
cartel cannot commit not to restrict output (and so a higher retailer price). As a result an
entrant may be unable to recoup entry costs in the presence of a retailer cartel, though it
may be able to in its absence. Thus, retailer collusion, by itself, may lead to exclusion to
the detriment of retailers (and to the benefit of the incumbent).
We also consider extensions that allow for differentiation, either at the retail level or
between the incumbent and entrant in the manufacturing segment. Beyond showing the
robustness of the results, these extensions highlight that competition (as captured by the
degree of differentiation between firms) in either the retail or the wholesale segment can
exacerbate or alleviate exclusionary pressure, depending on the degree of differentiation.
Aside from the RPM literature already discussed, another related literature is that on
naked exclusion arising from exclusive dealing arrangements (See Ch. 4 of Whinston (2006),
Rey and Tirole (2007) and Rey and Vergé (2008) for useful overviews). In this literature,
the closest papers to ours are Fumagalli and Motta (2006) and Simpson and Wickelgren
(2007), which explicitly consider exclusive dealing arrangements between manufacturers
and retailers. Earlier papers, by Rasmusen, Ramsayer and Wiley (1991) and Segal and
Whinston (2000) are distinct in assuming that buyers (equivalently, retailers) act as local
monopolists. Our setting differs from that presented in this line of research in that we
build on a repeated game framework instead of exploiting contractual externalities arising
from scale economies, although the coordination-style game that lies at the heart of this
literature finds a close analog in our setting. Our model is most distinctive in the ease with
which exclusion can occur in intensely competitive markets (i.e., Bertrand). In Simpson and
Wickelgren’s (2007) model, exclusion in intensely competitive markets requires exclusive
dealing contracts to be contingent on the actions of other retailers. As in Argenton (2010),
who allows for vertical quality differentiation, and Abito and Wright (2008), who allow for
downstream differentiation, in our environment, should the entrant succeed in entering,
5
the incumbent remains present as a competitive pressure in the market rather than leaving
the new entrant as an unfettered monopolist. In addition, the entrant poses no direct
competitive pressure unless accommodated by a retailer. These are key assumptions for
our analysis. We comment further on the relationship between our model and this literature
in the conclusion.
In the remainder of this paper, we first briefly review an older literature on RPM
and exclusion, which includes discussion of some empirical examples. Then in Section
3, we carefully describe the model, which relies on a two-state infinitely repeated game
(see Mailath and Samuelson (2006) for a comprehensive treatment of repeated games). In
Section 4, we present properties of the equilibria of the model and highlight the possibility
of equilibria in which the more efficient entrant is excluded. Sections 4.1 and 4.2 consider
welfare implications of the model and derive a simple bound on the extent of harm, which we
evaluate in a parameterized version of the model. In Section 5, we compare the incumbent’s
preference for exclusion over accommodating entry and colluding. Iin Section 6, we extend
the framework and, in particular, discuss differentiation among retailers and between the
entrant and incumbent. Finally, in Section 7, we draw out policy implications of the
analysis, including some implications for screens indicating the potential for exclusion.
2
RPM and exclusion
The idea that RPM may have exclusionary effects has a long history in the economics
literature. As early as 1939, Ralph Cassady, Jr. remarked on the potential for distributors
to favor those products on which they were getting significant margins via RPM, noting
that since “manufacturers are now in a real sense their allies, the distributors are willing
(nay, anxious!) to place their sales promotional effort behind these products, many times to
the absolute exclusion of non-nationally advertised competing products”(Cassady (1939, p.
460)). Cassady’s remarks are interesting in that they suggest a complementarity between
some of the pro-efficiency reasons for RPM and exclusion.12
Following Cassady’s early remarks, the potential for RPM to be viewed as an exclu12
Indeed, as discussed above, Klein and Murphy (1988) highlight that a manufacturer’s threat to withhold
super-normal profits can be efficiency-enhancing by helping to ensure appropriate service at the retailer level.
Instead, our paper argues that the possibility of losing these super-normal profits as a result of a changing
market structure can lead to exclusion of an efficient manufacturer. To the extent that efficiency-enhancing
rationales are more effectively implemented when more surplus is available, our framework would also
suggest a complementarity between the “pro-efficiency” rationales and exclusion.
6
sionary device did not surface again until the 1950s with the work of Ward Bowman in
(1955) and Basil Yamey in (1954). Yamey describes a “reciprocating” role of price maintenance whereby, “(t)he bulk of the distributive trade is likely to be satisfied, and may try
to avoid any course of action, such as supporting new competitors, which may disturb the
main support of their security”(1954 p. 22). Yamey (1966) also raises the possibility of
exclusion, suggesting that “Resale Price Maintenance can serve the purposes of a group
of manufacturers acting together in restraint of competition by being part of a bargain
with associations of established dealers to induce the latter not to handle the competing
products of excluded manufacturers”(p. 10). The quote is particularly interesting in its
suggestion of some complementarity between the possibility that RPM facilitates collusion,
and the exclusionary effect. Gammelgaard (1958), Zerbe (1969) and Eichner (1969) make
similar suggestions regarding the possibility of exclusion . More recently, following the Leegin decision, Elzinga and Mills (2008) and Brennan (2008) have discussed the exclusionary
aspect of RPM that is mentioned in the majority judgement.13
Bowman (1955) describes several examples of RPM’s use for exclusionary purposes, involving wallpaper, enameled iron ware, whiskey and watch cases. Many of these examples
are drawn from early antitrust cases and involve a cartel, rather than a monopolist firm,
as the upstream manufacturer instigating exclusion. Bowman also gives a few examples
of implicit upstream collusion rather than explicit cartelization and the use of RPM for
exclusion; specifically, he highlights the cases of fashion patterns and spark plugs. Given
that a cartel will wish to mimic the monopolist as much as possible, these examples are
consistent with the setting considered in this model. They also underline the complementarities between the view that RPM facilitates collusion, and the exclusionary perspective
articulated here.
These cases often involve contracts that include more-explicit exclusionary terms in
conjunction with the use of RPM. For example, in 1892, the Distilling and Cattle Feeding
Company, an Illinois corporation, controlled (through purchase or lease) 75-100 percent
of the distilled spirits manufactured and sold in the U.S. It sold its products (through
distributing agents) to dealers who were promised a five- cents-per-gallon rebate provided
that the dealers sold at no lower than prescribed list prices and purchased all their distillery
products from their (exclusive) distributing agents.14
Another well-documented example is that of the American Sugar Refining Company,
13
14
None of the papers mentioned here develops a formal model.
As recorded in U.S v. Greenhut et al. 50 Fed., 469, and U.S v. Greenhut et al. 51 Fed., 205.
7
discussed at some length by Zerbe (1969) (see, also, Marvel and McCafferty (1985)). The
American Sugar Refining Company was a trust formed in 1887 that combined sugar-refining
operations totaling, at the time of combination, approximately 80 percent of the industry’s
refining capacity. The principle purpose of the trust was to control the price and output
of refined sugar in the U.S..15 After a wave of entry and consolidation, by 1892, the trust
controlled 95 percent of U.S. refining capacity. In 1895, the wholesale grocers who bought
the trust’s refined sugar proposed an RPM agreement. Zerbe reports that the proposal
came in the form of “a threat and a bribe”: The bribe was that, in return for the margins
created by the RPM agreement, the grocers would not provide retail services to any refiner
outside the trust. The threat was in the form of a boycott if the trust refused to enter
into the RPM agreement. The exclusionary effect of the RPM agreement was only partial
at best: In 1898, Arbuckle, a coffee manufacturer, successfully entered the sugar-refining
business. In some regions, Arbuckle was unable to get access to wholesale grocers and
had to deal directly with retailers. Thus, while not prohibiting entry, the RPM agreement
may have raised the costs of this new competitor to the trust. Ironically, after several
years of cutthroat competition, Arbuckle and the trust entered into a cartel agreement
that persisted in one form or another until the beginning of the First World War.
The sugar trust is informative in that it involves RPM’s use in a setting in which
the product is essentially homogeneous (see Marvel and McCafferty (1985) for a chemical
analysis supporting this claim) and the manufacturer has close to complete control of
existing output. The lack of product differentiation makes theories of RPM enhancing
service or other non-price aspects of inter-brand competition difficult to reconcile with
the facts. Clearly, there was no reason to use RPM to facilitate collusion on the part
of refiners, since the trust already had achieved that end. The grocers may well have
wanted to facilitate collusion at their end, but the openness with which they negotiated
with the trust suggests that it was more in the spirit of good-natured extortion: a margin
in exchange for blocking entry.
The sugar example fits the setting considered in our model, in which an incumbent
monopolist faces entry by a lower-cost entrant. All products are homogeneous, and there
is no differentiation between retailers. This gives the model the flavor of cutthroat competition familiar from standard Bertrand price competition models. In particular, there is no
scope for service on the part of retailers, and the manufacturer easily solves the classical
15
See Zerbe (1969, p. 349), reporting testimony given to the House Ways and Means Committee by
Havermeyer, one of the trustees.
8
double-marginalization problems by simply using more than one retailer. If the entrant
enters, then retailers and the incumbent see profits decrease (to zero), and the entrant
captures market demand at a price equal to the incumbent’s marginal cost. To deter this
entry, the incumbent offers an RPM agreement which, over time, more than compensates
the retailers for any one-off access payment that the entrant may be able to afford. At its
heart, the RPM agreement is successful in that it forces individual retailers to internalize the impact of competition on the profitability of the incumbent’s product and on the
margins of all retailers. A feature of the model, which sits well with the sugar example,
is that both the incumbent and the retailers benefit from the RPM-induced exclusion. In
this sense, the fact that the grocers suggested the RPM agreement in the sugar example—
in contrast to the whiskey example in which the upstream firm initiated the agreement—is
entirely consistent with the exclusionary effect explored here.
3
The baseline model
There are two manufacturers who produce identical goods. One manufacturer is already
active in the market (the incumbent) and another is a potential entrant (the entrant). The
incumbent’s constant marginal cost of manufacturing is given by ci and the entrant’s by ce
m
where ci ≥ ce ≥ 0. We assume that ci < pm
e where pe is the price that would be charged
by a monopoly with cost ce . In order to enter the market, the entrant has to sink a fixed
cost of entry Fe ≥ 0. In practice, this fixed cost may be difficult for an antitrust authority
to evaluate and turns out to play a limited role in our baseline analysis; consequently, in
the analysis, we often focus on the limiting case where Fe = 0. It is important, however,
that the entrant is considered to be present in the market only if a retailer accommodates
entry—i.e., an entrant is not perceived to have entered until its products are available to
final consumers.16
There are n ≥ 2 retailers in this market. Retailers are perfect substitutes for each other,
and their only marginal costs are the wholesale prices that they pay to the manufacturers.
Lastly, total market demand in each period in this market is given by q (p).
Contracting between manufacturers and retailers occurs on two fronts: first, when the
entrant seeks to obtain a retail presence; and, second, when a manufacturer sells its product
to a retailer (that is, when exchange occurs). Each setting is dealt with in more detail in
16
We assume that vertical integration is prohibitively costly. We also assume that a merger or acquisition
of the incumbent by the entrant is not feasible.
9
the next two paragraphs.
As described above, for the entrant to gain a retail presence, at least one retailer must
agree to stock the product. This means that the retailer must be better off stocking the
product than not. To this end, the entrant can offer any form of payment (lump sum or
otherwise) to induce a retailer to carry its product.17 Once a retailer has agreed to stock a
product, it is always stocked. If the entrant’s product is stocked by a retailer, the entrant
joins the incumbent in the set of (perpetually) active firms.18
Conditional on being present in the market, a manufacturer sells to retailers via a perunit wholesale price, wi or we depending on whether the price is set by the incumbent or
the entrant. Manufacturers are not permitted to price discriminate across retailers or over
the quantity sold.19 Each manufacturer also has the option of setting a per-unit minimum
retail price.20 Without loss of generality, we can suppose that the manufacturer always
sets the retail price pi or pe .21 We say that a manufacturer imposes RPM if this price is
different from the one that any retailer would choose. The rationale for this definition is
that if an unfettered retailer would, independently, charge the price that a manufacturer
preferred, with no need for any (potentially costly) monitoring or enforcement, then RPM
plays no role.
17
The contract space is left unrestricted here, as no further structure is required. If the entrant were
limited to only offering transfers indirectly (for example, through a relatively low wholesale price), this would
only make it more difficult for the entrant to transfer surplus and compensate the retailer for accommodating
its entry. Thus, in making this assumption, we analyze the extreme case that makes it as difficult as possible
for the incumbent to foreclose entry.
18
That is, a firm has to sink the fixed cost of entry only once.
19
In the model, there is no incentive to discriminate across retailers, so this assumption is not restrictive.
The restriction on discrimination on the basis of quantity sold may be more restrictive. For instance, Marx
and Shaffer (2004) and Chen and Shaffer (2009) suggest that minimum share agreements may have an
exclusionary effect.
20
None of our arguments in the baseline model involves a manufacturer setting a maximum retail price
limit. Minimum retail prices are necessary for exclusion in our framework and in formulating necessary and
sufficient conditions for exclusion to be possible. We briefly consider a role for maximum retail prices in
Footnote 37 below.
21
In this setting, the retailers will always be weakly better off accepting the RPM agreements that the
manufacturers want to formulate; hence the retailer’s acceptance of the RPM agreement is assumed. While
a more complicated bargaining structure between the retailer and incumbent could be considered, for
expositional ease, we have implicitly employed a structure where the incumbent makes a take-it-or-leave-it
offer to all retailers simultaneously.
10
3.1
Timing
The model is an infinitely repeated game. All firms discount future profits with discount
factor δ.22
Figure 1 shows the structure of moves within a period, assuming only two retailers;23
transitions between periods are indicated by a dotted line and the updating of the period
counter, t = t + 1. There are two possible types of period, corresponding to different
states of the manufacturer market, which we label M (incumbent monopolist), and C
(competition). The game begins in state M at t = 1. In this period, the incumbent is
active, but the entrant has yet to decide to enter. This period begins at node iM , with
the incumbent setting a minimum retail price and a corresponding wholesale price (pi , wi )
for all retailers. Then, at node eM1 , the entrant attempts to enter by offering a transfer
R ∈ [0, ∞), payable to a single retailer and committing to an associated minimum retail
price and a corresponding wholesale price (pe , we ). The dash box in Figure 1 indicates an
information set so that retailers (r1 and r2 ) simultaneously choose to accept (accommodate
entry) or reject the entrant’s offer (if more than one accepts, then the recipient is chosen at
random). If no retailer accommodates the entrant, then transactions occur, period profits
are realized, and the period ends, with the state of the manufacturer market in the next
period continuing to be M; otherwise, if at least one retailer accommodates, then at node
eM2 , the entrant can choose either to pay the fixed cost Fe or not. Following that decision,
transactions occur, period profits are realized and the next period begins, though this next
period will be a competitive period, in which the state is C, if the entrant incurs the fixed
cost.
A period of state C involves a simultaneous move game in which both the incumbent
and entrant compete by setting a minimum retail price (should they wish) and a wholesale
price.
Note that in this timing, we suppose that the fixed cost of entry is paid only if a retailer
accommodates entry; this is a realistic assumption, for example, if the entrant needs access
to final consumers for final product configuration or for the marketing of a new-product
launch. Similar results apply if the fixed costs of entry are paid ex-ante as long as the
entrant is not considered active until a retailer has accommodated the entrant.24 We
22
Realistic values for δ depend, as in all repeated games, on the interpretation of a “period,” which should
be thought of as the length of time it takes for firms in a market to react to a change in circumstances.
23
Figure 1 shows two retailers for expositional ease only. All arguments apply to the n-retailer case.
24
There would, therefore, be three states of the game. In addition to M (where the incumbent has not
11
present the timing with fixed costs paid only after accommodation, first, since the analysis
is a little simpler and, second, since this timing reinforces the importance and central role
of retailer accommodation.
t=t+1
t.= t + 1
C
......................
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... ...
... ...
.. ..
.. ..
@
@
.. ..
.. ..
@ R, (we , pe )
@ (we , pe )
... ...
... ...
.. ..
.. ..
.
.
.
.. ..
..
.. ..
Q r1M
.. ..
... ...
.
Q Y
. .................
N
Q
.
... ...
.
Q
..
.. ..
Q
r2M
..
.. ..
...
... ...
@
@
..
.. ..
@ Y
@ Y
.. .. N
..
N
@..
@..
..
...
... ... ..
.. .. ..
..
..
..
..
................................
..
..
..
.. ........
...
...
...
.. eM2
...
...
..
..
@
..
..
0
@ Fe
...
...
..
..
@..
..
..
..
..
..
.
.
...........
.
- ..
...............................
......................
Figure 1: A schematic of the sequence of moves within periods and the transitions from
one state to another, with two retailers.
The transfer R serves as an inducement to a retailer to carry the entrant’s product. We
restrict this transfer to be paid only to one retailer, but given that all retailers are perfect
substitutes, this is not restrictive: To minimize the cost of entry, the entrant would want to
pay a transfer to only one retailer, since having one retailer offers the same market access
as having many.
What is crucial is the requirement that at least one retailer agree to carry the entrant’s
good for the entrant to become active. Hence, the transition from the state of the market
M to state C requires a retailer to agree to stock the entrant’s product. The effect of such
an agreement, which is effectively an assurance of perpetual market access, is to guarantee
entered), and C (where there is competition between incumbent and monopolist), there could be periods
where the entrant has sunk its fixed costs of entry, but no retailer has yet accommodated entry.
12
competition between the two manufacturers in all periods post-entry; in particular, it is
assumed that following entry, the incumbent remains present as a competitive threat that
does not require retailer-accommodation.
4
Analysis
Before analyzing the game outlined in Section 3, consider the behavior of an incumbent
with no threat of entry. In the absence of RPM, Bertrand competition among retailers
ensures that the retail price will simply be equal to the wholesale price that the incumbent
manufacturer charged. The incumbent can, therefore, charge a wholesale price equal to its
monopoly price pm
i = arg max(p − ci )q(p) and earn monopoly profits. It can do no better
with RPM, and so without the threat of entry, in this model, RPM plays no role.25
We characterize the Markov Perfect Nash equilibria of this game, where the states
are given by the type of the current market structure. That is, following the notation in
Figure 1, the state space is the finite set {M, C}. We use Markov Perfection to remove the
possibility of firms’ colluding post-entry. However, note that since a “deviating” retailer
who accommodates entry changes the state from M to C, the equilibrium play in state M
resembles a collusive outcome among retailers—we highlight that this can be beneficial for
the incumbent manufacturer in excluding a rival.26 We first consider the absorbing state
following entry (that is, the state C) and then turn to consider the entry decision (state
M ).
Suppose that the state is C, so that the period game has both the entrant and the
incumbent active and simultaneously setting (wi , pi ) and (we , pe ). Since the manufacturers’
goods are identical and the retailers are perfect substitutes, the equilibrium resembles a
standard Bertrand equilibrium. The equilibrium has the wholesale price set at the marginal
cost of the less efficient incumbent (ci ) and all retailers purchasing at this price from the
more efficient entrant—i.e., we = wi = ci .27 The retail price (which, in the model, we
assume is determined by manufacturers through RPM) will also be set at ci since at any
25
Indeed, this reasoning has led some commentators to suggest that a monopolist’s use of RPM reflects
that retail service is an important factor (see, for example, Winter 2009).
26
The interaction between collusion and resale price maintenance is explored in Jullien and Rey (2007).
27
Since the entrant’s cost is lower than the incumbent’s, there are actually a range of equilibria that
involve the incumbent’s pricing between ce and ci and the entrant just undercutting. As is standard, we
ignore these equilibria since they involve weakly-dominated strategies that make little empirical sense and
are not robust to trembling-hand style equilibrium refinements.
13
higher price, any manufacturer could attract all the retail customers by undercutting by an
epsilon increment. The entrant has no incentive to force a lower price since it is assumed
m
that ci < pm
e where pe is the price that would be charged by a monopoly with cost ce .
Note that Bertrand competition among retailers (since they are perfect substitutes) implies
that RPM plays no role in this case and that competition among retailers is intense, in
the sense that they earn no profits. The same outcome would arise—that is, retailers
would set a retail price equal to we (= ci )—whether or not the entrant used RPM, and so
according to our definition, here there is no RPM. Since our equilibrium concept is Markov
Perfection, there is no way to sustain pricing above ci : The state-space does not admit the
possibility of collusion and a punishment phase that could be used to deter undercutting.
This reasoning yields the following result.28
Lemma 1 Post-entry (that is, when the state is equal to C) per-period profits are:
1. πiEntry = 0 for the incumbent;
2. πrEntry = 0 for any retailer; and
3. πeEntry = (ci − ce )q(ci ) for the entrant.
Given this characterization for periods following entry, we can turn to characterize
the full game. Our interest is in highlighting when exclusion via RPM is possible in
equilibrium. However, there is always an equilibrium with no exclusion. This equilibrium
need not involve RPM and, so, its existence does not further our understanding of RPM
in any way.29
Lemma 2 There is always an equilibrium in which entry takes place in the first period (in
state M ). In such an equilibrium, RPM serves no purpose and is not observed.
28
Shaffer (1991) considers a model that is analogous to our state C, but interprets RPM as incorporating a form of commitment that is more binding than merely setting a wholesale price, so that if one
firm uses RPM and the other does not, a leader-follower pricing game emerges. This interpretation may
change the equilibrium payoffs. We have not adopted this interpretation, and so our state C is always a
simultaneous-move game. Adopting Shaffer’s interpretation would not qualitatively change the analysis in
the baseline model. In the extensions that consider differentiation, this alternate view would change the
analysis somewhat but not the qualitative results.
29
This equilibrium is one in a set of equilibria in which no exclusion occurs. Some of these equilibria can
involve RPM, but not in a way that is economically meaningful (see the next footnote). For this reason, we
do not dwell on these equilibria. Lemma 2 makes the point that at least one non-exclusionary equilibrium
will exist, which is sufficient for our purposes.
14
Proof. Consider a period where the state of the market is M, and consider that part of the
period in which retailers simultaneously choose whether to accept or reject the entrant’s
offer of R. If one retailer accepts the entrant’s offer, then the best response set of all other
retailers will also include accept. This is because acceptance by one retailer ensures that
entry occurs. If one retailer accommodates entry, then the entrant will get access to the
market and be able to generate a retail price that undercuts all retailers that supply the
incumbent’s good. This steals the market from the incumbent and retailers who sell the
incumbent’s good. Given this entry, retailers anticipate making no profit in the current
or future periods (following Lemma 1), and so it is weakly optimal to accommodate and
strictly so if the entrant offers any R > 0. It follows that there is an equilibrium in which
the entrant offers R = 0 and all retailers accept this offer. Since the incumbent makes no
profit if entry occurs, pi = wi = ci is a best response, resulting in pe = we = ci ; that is, no
RPM (since if we = ci , then Bertrand competition among retailers would lead to the same
retail price).30
We now to turn to the necessary and sufficient conditions for an exclusionary equilibrium to exist. By exclusionary, we mean an equilibrium in which the retailers never
accommodate entry. We show that the presence of minimum RPM can generate this exclusion.
Entry depends on whether a retailer will agree to carry the entrant’s products. Hence,
the retailers” equilibrium strategies in state M are determinative. It is helpful to examine
this part of the game more closely. This is done using Figure 2, which represents the
retailers’ payoffs, conditional on their action and that of the other retailers. These actions
are either to accept the entrant’s offer and accommodate it (Y ) or to reject it (N ). As
in Figure 1, Figure 2 assumes only two retailers, but all arguments are valid for n ≥ 2
retailers, and are, where useful, stated as such.
Note that since retailers are symmetric, the payoff matrix in Figure 2 is symmetric.
Payoffs are represented by, for example, π (Y, N ), where Y is the action of the retailer and
30
In fact, due to the sequential structure of the game, any pi > ce is also a best response by the incumbent,
since it also yields zero profit. pi > ce may be a consequence of wi = pi , or due to wi < pi and the use of
RPM. This leads to a range of equilibria with pi ∈ [ce , ∞] and pe = min {pm
e , pi } However, as is standard,
we focus on pi = wi = ci as the most reasonable case.
In particular, the use of RPM by the incumbent, in an equilibrium in which pi > ci , would only benefit
the entrant by allowing additional profits to be earned in the entry period. Though theoretically possible,
these seem perverse and unlikely equilibria that do not speak to our central concern of how RPM may
facilitate exclusion.
15
N is the action of the other retailer. Note that if π(N, Y ) ≤ π(Y, Y ), then there is always
an equilibrium where both retailers wil choose Y —that is, where entry is accommodated.
Lemma 2 points out that the game is structured so that this condition can always be
met (with π(N, Y ) = π(Y, Y ) = 0). The existence of this equilibrium, however, does
not imply that this equilibrium is unique. Exclusion is also an equilibrium if there are
optimal strategies by the manufacturers such that, for retailers, π(N, N ) ≥ π(Y, N ). An
exclusionary equilibrium arises when the retailers coordinate on this (N, N ). It can be
supported in equilibrium whenever the cost to the entrant of raising π(Y, N ) above π(N, N )
is prohibitive, so that it prefers not to incur the fixed cost of entry.
Retailer 2
N
Y
π (N, N )
π (Y, N )
N
π (N, N )
π (N, Y )
Retailer 1
π (N, Y )
π (Y, Y )
Y
π (Y, N )
π (Y, Y )
Figure 2: The retailers’ payoff matrix.
Since exclusion results in a zero profit for the entrant, the entrant will always be happy
to transfer as much surplus as is required to make sure that π (Y, N ) > π(N, N ) if the
alternative is exclusion, subject to meeting a non-negative discounted-profit-stream constraint.31 The maximal surplus that the entrant could transfer to a retailer is given by first
covering the fixed cost of entry and then transferring as much as possible of the maximal
profit that can be earned in the current period, if entry occurs, plus the discounted value
of all future profits in state C. The latter is easily determined given the characterization of
per-period profits in Lemma 1. To compute the former, note that if the incumbent offers
31
Note that we assume away any frictions in capital markets.
16
(wi , pi ), then the entrant would maximize its surplus extraction in the current period by
32 Thus, the maximal value of π (Y, N ) that the
setting a retail price of p̂e = min {pi , pm
e }.
entrant can generate is
max π (Y, N ) = (p̂e − ce ) q (p̂e ) +
δ
(ci − ce ) q (ci ) − Fe .
1−δ
This can be implemented, for example, by setting we = ce and R =
δ
1−δ
(1)
(ci − ce ) q (ci ) − Fe .
We now turn to the incumbent’s problem and, in particular, we consider the maximal
value of π(N, N ) − max π(Y, N ), subject to the incumbent’s making non-negative profits,
to address the question of whether the incumbent can foreclose entry. In practice, the
incumbent would wish the retailers to earn only enough profits that they would prefer
not to accommodate entry—that is, so that π(N, N ) = max π(Y, N )—and keep any additional profits; however, comparing max π(N, N ) − max π(Y, N ) as defined in (1) determines
whether exclusion is possible. That is, it provides necessary and sufficient conditions for
the existence of an exclusionary equilibrium.
Note that π (N, N ) is simply determined as the discounted value of the stream of surplus
that accrues to the retailers if all retailers deny access—that is,
the factor
1
n
1 1
1−δ n (pi
− wi )q(pi ), where
reflects the fact that the n retailers share the market evenly when charging
the same retail price. Note that since pi can affect p̂e and, thereby, affect max π (Y, N ), as
defined in (1), the problem need not reduce to choosing pi and wi to maximize (pi −wi )q(pi );
however, wi does not affect the entrant’s problem and so, clearly, the incumbent would
choose wi = ci to guarantee itself non-negative profits and guarantee retailers all the
surplus generated. The incumbent’s problem, therefore, is reduced to choosing pi in order
to maximize
δ
1 1
(pi − c)q(pi ) − (p̂e − ce ) q (p̂e ) +
(ci − ce ) q (ci ) − Fe .
1−δn
1−δ
(2)
m
First note that if pi ≥ pm
e , then the problem is trivially solved by setting pi . Consider,
instead, the case pm
e > pi , and note that, the above expression can be rewritten as
max (
pi <pm
e
1 1
δ
− 1)(pi − ci )q(pi ) − (ci − ce )q(pi ) −
(ci − ce )q(ci ) + Fe .
1−δn
1−δ
(3)
32
Note that the entrant’s wholesale price is irrelevant in determining the maximum that the entrant can
transfer to a retailer since any profits (we − ce )q(b
pe ) that the entrant earns can either be transferred as part
of the lump sum R or through choosing we = ce instead.
17
If
1 1
1−δ n
m
> 1, then, since pi < pm
e ≤ pi , the incumbent prefers to set pi as high as
possible, both to make the first term, in the expression above, larger and to make the
second term smaller. However, this corner solution takes us back to the previous case,
where the incumbent would prefer to set pi = pm
i . Instead, if
1 1
1−δ n
< 1, then regardless of
the incumbent’s choice
max (
pi <pm
e
1 1
δ
− 1)(pi − ci )q(pi ) − (ci − ce )q(pi ) −
(ci − ce )q(ci ) < 0
1−δn
1−δ
,
and so as long as Fe is small enough, the incumbent can never foreclose entry.33
This discussion establishes the following:
Proposition 1 Suppose that
1 1
1−δ n
> 1. Then, an exclusionary equilibrium (one in which
the entrant does not enter) exists if and only if
Fe +
If
1 1
1−δ n
1 1 m
δ
m
m
(pi − ci ) q (pm
(ci − ce ) q (ci ) .
i ) ≥ (pe − ce ) q (pe ) +
1−δn
1−δ
(4)
< 1 and fixed costs, Fe , are sufficiently small, there is never an exclusionary
equilibrium.
The following corollary is immediate.
Corollary 1 An entrant with marginal cost ce = ci can always be excluded if
4.1
1
1−δ
≥ n.
The distortionary effect of exclusionary RPM
In this setting, the efficiency cost of an exclusionary minimum RPM agreement comes from
two sources.
First, there is the productive efficiency loss from having a low-cost manufacturer excluded from the market. In the baseline model, above, the per-period loss in producer
surplus from this exclusion is (ci − ce ) q (ci ).
The second source of inefficiency is due to a loss of consumer surplus. As argued
in the paragraphs leading to Lemma 1, the retail price of the good, if entry occurs, is
33
1
Note that meaningful exclusion may still occur. If Fe = 1−δ
(ci − ce ) q (ci ), then exclusion may still be
1 1
possible if 1−δ n < 1, depending on the parametrization of the model. This value of Fe is interesting, as it
is the highest value of Fe that would allow profitable entry if the incumbent were pricing at marginal cost.
18
given by ci . In examining the possibility of foreclosure, Proposition 1 determines when
exclusion is feasible. However, as long as the condition in Proposition 1 is met, there could
be many equilibria where entry is foreclosed. In all reasonable equilibria, however, the
retail price for the good is given by pm
i , with multiplicity arising from the differences in
the division of producer surplus between manufacturer and retailers, via the choice of the
wholesale price.34 Thus, the second source of welfare loss is the difference in consumer
surplus generated at p = pm
e and p = ci that is not captured by the incumbent as part of
its monopoly rent.
Thus, the efficiency loss from exclusionary RPM, in the baseline model of Section 3, is
given by
RPM Welfare Cost =
4.2
1
1−δ
Z
pm
i
[q (x) − q (pm
)]
dx
+
(c
−
c
)
q
(c
)
− Fe > 0.
i
e
i
i
(5)
ci
The range of exclusion
Next, we turn our attention to the range of costs that can be excluded using minimum
RPM in this manner. The upper bound on this range is given by Corollary 1 above. That
is, if
1
1−δ
≥ n, then the range of excluded costs is [ce , ce ], where ce = ci . To articulate the
lower bound, the value of Fe needs to be fixed. To examine the size of a ‘smallest’ range
of exclusion, we set Fe = 0.
Corollary 2 Provided that
1
1−δ
≥ n, the lowest marginal cost able to be excluded, ce , is
implicitly defined by
1
1
δ
m
m
(pm − ci ) q (pm
(ci − ce ) q (ci ) .
i ) = (pe − ce ) q (pe ) +
1−δ i
n
1−δ
(6)
The expression in Corollary 2 is perhaps more useful via the derivation of a bound on
ce . Note that
34
Formally, there may be other (unreasonable) equilibria that arise from the multiplicity and coordination
among retailers discussed in Section 4. For example, all retailers may play the (perverse but) equilibrium
strategy to deny entry only if the incumbent sets a retail price (pm
i − k) for some constant k low enough.
Then, the incumbent would impose a price of (pm
i − k) using RPM. We argue that the sort of equilibrium
selection process that is required by such an equilibrium is unconvincing. In any case, it does not undermine
our main point: that RPM can support exclusionary equilibria.
19
1
1
δ
m
m
(pm − ci ) q (pm
(ci − ce ) q (ci )
i ) = (pe (ce ) − ce ) q (pe (ce )) +
1−δ i
n
1−δ
δ
m
≥ (pm
(ci − ce ) q (ci ) ,
i − ci ) q (pi ) +
1−δ
which can be rearranged to yield
(ci − ce ) ≤
m
(pm
i − ci ) q (pi )
.
n
q (ci )
(7)
The empirical utility of this bound lies in the fact that it uses only information about
the incumbent firm. That is, it is based on information that is potentially estimable using
observable price and quantity data.
0.8!
0.8!
0.7!
0.7!
0.6!
0.6!
0.5!
0.5!
0.4!
0.4!
0.3!
0.3!
0.2!
0.2!
0.1!
0.1!
0!
0!
2! 3! 4! 5! 6! 7! 8! 9! 10!11!12!13!14!15!16!17!18!19!20!
2! 3! 4! 5! 6! 7! 8! 9! 10!11!12!13!14!15!16!17!18!19!20!
Notes: The horizontal axis is the number of retailers in the market. The vertical axis is the difference between ci = 4
and either the exact measure of ce (the grey column; ci − ce ) or the upper bound computed using Equation (7) (grey
and black columns combined). The left panel is constructed using the demand specification log(q) = 5.6391− 37 log(p),
while the right panel is constructed using the demand specification q = 10 − p. The marginal cost of the incumbent
is set equal to 4. The demand specifications generate the same monopoly price and quantity for the incumbent.
We have set δ = 0.95, which results in exclusion being impossible if the number of retailers is greater than 20 (see
Corollary 1).
Figure 3: The interval of excluded costs, and the bound.
20
A sense of the extent to which exclusion is possible from RPM can be obtained from
Figure 3, which compares the exact range of the excluded costs of the entrant for two
parametrizations of the model, as the number of retailers changes. The panel on the
left is computed using a constant elasticity demand curve, while the right uses a linear
specification. The specifications are generated so that the incumbent’s monopoly price in
both settings is the same. The marginal cost of the incumbent is equal to four. The grey
column shows the exact value of ci − ce given that ci = 4, while the black interval shows
the margin between the exact measure and the upper bound computed using equation (7).
The simulations suggest that the range of costs that can be excluded is sufficiently large
as to be economically meaningful. In the specification on the left (which uses a constant
elasticity demand specification), when there are two, five, and ten retailers, the range of
excluded costs is 10.2, 4.1, and 2.0 percent of the incumbent’s marginal cost, respectively.
In the specification in the right panel (which uses a linear demand specification), the
corresponding range of excluded costs is 18.8, 7.5, and 3.8 percent of the incumbent’s
marginal costs. Recall that these simulations assume that there are no fixed costs of entry
and, so, these likely underrepresent the extent of possible exclusion.
Particularly in markets where there are relatively few retailers and, hence, where the
exclusionary potential of a minimum RPM agreement is greatest, the bound appears to be
useful. When there are only two retailers, the additional range indicated by the bound is
seven and eight percent of the length of the true interval, for the constant elasticity and
linear specifications, respectively.
5
Exclusion vs collusion: Relaxing the Markov assumption
An important assumption in the baseline model is that of Markov Perfect Nash equilibrium
(MPNE). By restricting play to be the same in all periods with the same state, we rule out
collusion in the stage in which the entrant has entered. This is helpful for developing the
model and focuses attention on the equilibrium we illustrate.
However, our model might be thought of as one in which the incumbent synthesizes a
‘cartel’ among the retailers to enforce a particular market structure. Resale price maintenance assists the synthesis of this cartel-like structure by allowing the analog of a marketdivision scheme. This raises the question of whether other cartel structures might be
attractive. Answering this question in the context of this model requires that we relax the
MPNE restriction.
21
There are several ways coordination could manifest once the MPNE restriction is relaxed. First, the entrant and the retailers could try to exclude the incumbent in much
the same way as the incumbent excludes the entrant in the baseline model. In our model,
we assume that once entry occurs, a firm can get retail space, so such an exclusionary
strategy would involve a slight re-engineering of the model. Setting that aside, this form
of coordination would result in an exclusionary harm similar to that discussed in Section
4.1 and so involves only a slight re-statement of the problem.
Second, we might imagine that the incumbent accommodates entry and the manufacturers collude post-entry. We consider when the incumbent would choose to exclude entry,
rather than accommodate and collude, in the next subsection. Lastly, the retailers may
collude. We turn to this case after addressing manufacturer collusion.
5.1
Manufacturer collusion
We keep the retail sector as-is (i.e., competitive) and consider collusion among manufacturers post-entry. In doing so, we consider the scenario suggested by the cartel formed
by Arbuckle and the American Sugar Company following Arbuckle’s entry. The question
we ask is: Under what conditions would an incumbent prefer to exclude an entrant, when
colluding post-entry is an option?
One form of manufacturer collusion would involve the entrant simply paying off the incumbent for not producing at all. This is essentially an acquisition. Since we have assumed,
so far, that the entrant (for whatever reason) cannot buy out the incumbent, we consider a
different form of collusion. We consider collusion in which the manufacturers cannot make
explicit lump-sum payments to each other (that is, no sidepayments). Given this restriction, and retaining the assumption that the retail sector plays single-stage Bertrand, this
means that collusion is brought into effect by splitting the market in some way between
the entrant and incumbent (Harrington (1991) investigates the same cartel problem).
Specifically, we assume that the entrant and incumbent collude on the price and the
quantity that each provides to the market.35 Hence, the collusive agreement is over <
qe , qi > where the total market quantity, q, is equal to qi + qe , and the market price is
p (q). Employing a grim-trigger-strategy equilibrium, a collusive market split following
entry must satisfy the following condition for the entrant (with an analogous condition for
35
For an empirical analog, consider the lysine cartel described in de Roos (2006).
22
the incumbent):36
Entrant’s cooperation condition if p (q) < pm
e :
qe [p (q) − ce ] ≥ (1 − δ) q [p (q) − ce ] + δ (ci − ce ) q (ci )
(8)
Entrant’s cooperation condition if p (q) ≥ pm
e :
m
qe [p (q) − ce ] ≥ (1 − δ) q (pm
e ) [pe + ce ] + δ (ci − ce ) q (ci )
(9)
The entrant’s cooperation condition says that, if cooperation occurred in previous
rounds, the entrant will continue to cooperate (in which case, the return in each period is
their quantity allocation multiplied by the margin they earn) as long as the continuation
value from deviating is less than the return from cooperating. The continuation value
under a deviation is the one-period opportunity to just undercut the cartel price and meet
total market demand at that price, followed by profits in the stage game (as per Lemma
1) thereafter.
Faced with these conditions, there is a range of < qe , qi > combinations that the
manufacturer cartel can support. Lemma 3 below states an upper bound on the profit the
incumbent can earn in the incumbent-optimal cartel.
Lemma 3 An upper bound on the most that an incumbent can earn per period from colluding with an entrant is:
m
π Collude = δq (pm
e ) (pi − ci ) − δ (ci − ce ) q (ci )
(pm
i −ci )
(pm
e −ce )
This bound is
tight when ci = ce .
This bound is constructed by observing that the incumbent-optimal collusive agreement
m
involves setting a price between pm
e and pi , with the incumbent’s quantity set by making
the entrant’s cooperation condition bind. The bound is reached by setting the collusive
price equal to pm
i , but with the the quantity supplied by the industry as a whole consistent
with a price of pm
e (and noting that the incumbent’s quantity is decreasing in the price in
this range).
It follows from Proposition 1 that a tight upper bound on the profit that an incumbent
36
Here, consistent with our approach in Section 4, we restrict attention to strategies that are not weaklydominated; that is, we suppose that the incumbent does not set a price below ci . For an interesting analysis
of collusion with asymmetric firms that does not impose such a constraint, see Miklos-Thal (2010).
23
can enjoy in excluding an entrant is
m
m
m
π Exclude = (pm
i − ci ) q (pi ) − n [(1 − δ) (pe − ce ) q (pe ) + δ (ci − ce ) q (ci )] + (1 − δ) nFe .
On the assumption that the incumbent can get its optimal surplus under either scheme,
we can understand when the incumbent might prefer to exclude, rather than accommodate
and collude, by comparing π Exclude and π Collude .37
Examination of these conditions suggests that exclusion is attractive when entrants have
low marginal costs, but high fixed costs. To see this, consider two polar cases, first the case
m
where ce = ci . In this instance, the (best-case) return from collusion is δ (pm
i − ci ) q (pi ),
m
while the (best-case) return from exclusion is (nδ − 1) (pm
i − ci ) q (pi ), which is always
strictly less than the return from collusion, except when δ = 1 and n = 2.38 Next, consider
the case where ce is so low that pm
e = ci , but the fixed cost is so high as to make entry
marginal in a competitive environment (that is, Fe =
1
1−δ
(ci − ce ) q (ci )). In this instance,
the incumbent’s collusive return is equal to zero, while the exclusionary return is equal to
the incumbent’s monopoly profit.
The underlying force at work is that the entrant can not credibly commit to give the
incumbent a high collusive rent. Indeed, once entry has occurred and the fixed cost is
sunk, a low-cost entrant requires a high proportion of market quantity to be induced to
cooperate in a collusive agreement since the difference between the collusive payout and
the competitive payout is comparatively small. Any commitment to give the incumbent
a large share of any subsequent agreement would not be credible in the face of the temptation to deviate. However, prior to the fixed cost being sunk, it can be cheap for the
incumbent to exclude the entrant since the fixed cost offsets much of the rent that the
entrant might expect to entrant post entry (and this reduces how much the entrant can
afford to compensate retailers for accommodating).
Lastly, note that this argument was developed for the case where the incumbent faces
a single potential entrant. If the incumbent were to face many entrants, then exclusion
would continue to be equally effective, while accommodation and subsequent collusion
would become a markedly less attractive option. Thus, relative to manufacturer collusion,
37
One reason to prefer one over the other is the relative ease of coordinating exclusion and collusion, and
the surplus split provided under each. Here, we are examining where exclusion might be preferred, even
when collusion is most attractive.
38
Recall that fixed costs are assumed to be low enough to allow entry when the market is competitive,
when ci = ce that implies Fe = 0.
24
exclusion becomes more likely as potential entrants become more prolific.
5.2
Retailer collusion
We now turn to the possibility of the retailers forming a cartel in the product market, but
suppose that manufacturers set the wholesale price competitively.39 The retail cartel we
have in mind is supported by standard grim-trigger strategies in a repeated game. Figure 4
depicts the market following entry, when the retailers collude in the product market. The
retailers act like a monopolist, taking the wholesale price as given. Since the entrant has
the lower marginal cost, the outcome of competition (as in Lemma 1) is that the entrant
serves the wholesale market. However, the monopoly distortion coming from the retailers
means that some quantity less than q (ci ) gets demanded. That is, we observe standard
double marginalization. The amount transacted will either be q (pm
i ), if the entrant charges
a wholesale price of ci , or some quantity q̃ if it is profitable to drop the wholesale price to
induce the retail cartel to sell more quantity.
Regardless of the actual wholesale price the entrant sets, the entrant’s profit is less
than that described in Lemma 1 when everyone competes. That is, if everyone competes,
the entrant’s post-entry, pe- period, profit is represented by rectangle ABFE. However, if
the entrant charges a wholesale price of ci , profits are ABCD, and if the entrant charges a
wholesale price of p̃ < ci , then profits are GBJH.
Hence, if the fixed costs of entry are sufficiently high, such that (1 − δ)Fe is greater
than the post-entry, per-period profit when the retail cartel operates, then the entrant
will not enter. This, of course, is good news for the incumbent. Indeed, the presence of
the retail cartel can ensure that the incumbent need not expend resources on exclusion,
whether via RPM or otherwise. Instead, the only problem the incumbent faces is how to
mitigate the damage caused by the double-margin distortion imposed on its profits by the
retailer cartel. If maximum RPM is available, then this is an easy contractual solution (set
wi = p i = p m
i ). In the absence of maximum RPM, the incumbent still enjoys profits, and
possibly more than if it had to use RPM as an exclusionary device.
39
Another scenario might be that the retailers also use a repeated game mechanism to extract morefavorable terms from the manufacturers, wherein the threat to manufacturers might be to not stock the
product. This could occur in combination with product-market collusion. Examining this case, which seems
interesting and important, involves a substantial modeling exercise beyond the scope of this paper. We are
unaware of any papers that consider a retail sector colluding to extract rents from upstream manufacturers
and consumers simultaneously.
25
A@
A @
A @
A
@
A.........@
.
.
.
.
.
.
.
.
.
.
.
.
.....
pm
i
..
A
@
...
p̃m...............A................@
.. ... @
A
. .
A .... .... @
A ... ...
@
A .... ....
@
.
ci A
A... ...
@
D.
E.
..@
.
..A ..
..
... A ...
... @
..
G
... A...H
p̃ .............................
@
..
. ..
.
.
.
.
A
@
C. J.
F.
.
ce B
.
... ... A
.
@D
.
... ... A
...
.
. .
A
q (pm
q (ci )
i ) q̃
A MR
Figure 4: Pricing by a retailer cartel and the entrant’s wholesale price response.
An important point is that the cartel suffers from not having the entrant in the market,
since, with the entrant active, the whole price must decrease. This raises the question of
why the retail cartel does not accommodate entry. The problem is that retailers are unable
to commit to not colluding post-entry, and, hence, even if they are keen to accommodate
the entrant, the entrant will stay away. Faced with this commitment problem, the retailers
might be able to subsidize entry using a lump-sum transfer or increase their ability to
commit to not colluding by using antitrust regulators and inviting regulatory scrutiny via,
say, whistle-blowing behavior. Of course, either of these measures involves costs on the
part of the retailers and, depending on the parameters, may not be worthwhile.
Hence, collusion by the retailers in the product market creates a series of problems that
can work to the incumbent’s advantage. Indeed, in the case illustrated here, it can remove
the need for minimum RPM as an exclusionary device altogether. Instead, maximum RPM
becomes useful to the incumbent to mitigate the distortion caused by the cartel, resulting
in highly profitable exclusion.40
40
When two manufacturers are present, reasoning analogous to that used in Lemma 1 implies that
maximum RPM ceases to be useful.
26
6
Differentiation
Our baseline model is deliberately stark and simple in order to aid the presentation; however, the intuitions and economic forces apply more generally. In particular, in this section,
we extend it first by allowing for differentiation between the incumbent and entrant manufacturers in Section 6.1, and then by allowing for differentiation among the downstream
retailers in Section 6.2. These extensions not only show the robustness of our central
result—that RPM can be used for upstream exclusion—but also provide additional insight
in highlighting that stiffer competition (through greater substitution at either the upstream
or the downstream market) has subtle and non-monotonic effects.41
In order to provide analytic results, we consider firms that are differentiated along a
Hotelling line with uniformly distributed consumers; however, first, we step back from
the modeling details and highlight that, analogous to the baseline model, we can consider
whether the incumbent can profitably exclude an entrant by breaking down the problem
to characterizing the maximal static profits under the different possible market structures:
(i) where the incumbent is a monopolist, (ii) in a period where a retailer accommodates
the entrant, and (iii) in post-entry competition between the incumbent and entrant. We
denote the per-period retailer profits under the most generous RPM arrangement that the
incumbent can profitably offer by πrRP M ; the payoffs to retailers and the entrant in a postentry period by πrpost and πepost , respectively; and the maximal combined payoffs for the
entrant and accommodating retailer, in a period in which the entrant is accommodated by
m .42
πac
Following the logic of the baseline model, there is an equilibrium where the incumbent
can foreclose entry using RPM whenever every retailer prefers to continue with the most
generous RPM arrangement rather than to accommodate the entrant even under the most
m and the net
generous terms that the entrant can offer (which involves transferring all of πac
present value of its post-entry profits net of fixed entry costs). It is convenient for presentation to assume that entry costs are equal to zero, in which case there is an equilibrium
with entry foreclosure as long as
1
RP M
1−δ πr
m +
> πac
41
post
δ
1−δ πe
+
post
δ
1−δ πr
or, equivalently,
Another extension would be to consider two differentiated incumbent manufacturers, and investigate
their incentive to exclude. As should be clear, the basic mechanism will persist should the incumbents be
sufficiently differentiated.
42
Note that in the baseline model, πrpost = 0 since in that model retailers are homogeneous and compete
in prices. When we allow for differentiated retailers below, πrpost > 0.
27
m
πrRP M > (1 − δ)πac
+ δ(πepost + πrpost ).
6.1
(10)
Upstream differentiation
In this section, we extend the baseline by allowing for differentiation between the incumbent and entrant manufacturers. We suppose that retailers are undifferentiated and allow
retailers to stock both of the upstream products. Clearly, a little differentiation has little
impact on the foreclosure condition in expression (10), as compared to the baseline model;
however, in this section, we also highlight that as differentiation increases, Condition (10)
changes in important ways, and it can become either more difficult or easier to satisfy.
First, note that, as in the baseline case, πrpost = 0 since there is Bertrand competition
among retailers. In the post-entry game (state C), all retailers can stock both types of
product, and Bertrand competition leads all retailers to price each product at the wholesale
price and so erode all their profits. Also, note that differentiation between the entrant and
the incumbent has no impact on profitability if the entrant is absent from the market; that
is, πrRP M is independent of the degree of differentiation.
It follows that differentiation affects the foreclosure condition in expression (10) only
m and π post . It is sufficient to consider π post (and δ close to 1) to
through its effect on πac
e
e
gain intuition for why differentiation can have non-monotonic effects on Condition (10).
More differentiation can either increase or decrease the entrant’s post-entry profits: If the
entrant is much more efficient than the incumbent, then he may prefer little differentiation,
as this would allow him to poach the incumbent’s customers cheaply; instead, if the entrant
and incumbent are competing on relatively level terms, then differentiation will weaken
price competition in the post-entry game, and so increase the entrant’s profits. That is,
depending on the differences in costs, the entrant may either prefer to grab the entire
market for a low price, or some of the market for a relatively high price.
These intuitions can be analytically illustrated by formally modeling and parameterizing the extent of differentiation between the incumbent and entrant manufacturers. We
do so by adopting a standard Hotelling framework, where final consumers have preferences
that are uniformly distributed along a line of length 1. The incumbent is located at 0, and
the entrant is located at α ∈ [0, 1] along the line. Consumers face quadratic transport costs
in consuming a product that is not at their ideal location; specifically, a consumer who is
located at x gains net utility M − x2 − pi from purchasing from the incumbent at price pi
28
and gains M − (α − x)2 − pe from purchasing from the entrant at price pe . We suppose
that M is sufficiently high that the market is always covered by a monopolist.
The available strategies and the timing of the game are identical to those considered
in our baseline model, and the analysis proceeds in a similar fashion. The characterization
of profits is a little more involved than in the baseline case, and we summarize the results
in Lemma 4. Its proof is somewhat mechanical and appears in the Appendix. We assume
throughout that the market is fully covered (which, here, requires that M > 3 + ci ).
i
Lemma 4 Maximal profits under different
market structures are given by πrRP M = M −1−c
,
n

2

 1 (4α−ce +ci −α2 )
if α(2 + α) > ci − ce > α(2 − 5α)
post
post
m
2
18
α
.
πac = M −1−α −ce , πr = 0 and πe =

 ci − ce − α2
otherwise
Lemma 4 allows us to populate Condition (10). In particular, it allows us to show
that entry can be excluded when the upstream manufacturers are differentiated and that
differentiation (greater α) can have a non-monotonic impact on the incumbent’s ability to
exclude the entrant. Confirming the general intuition discussed above that differentiation
may either increase or decrease post-entry profits, depending on whether competitionsoftening or business-stealing dominate, it is immediate following the characterization in
d post
= −2α; instead, consider the case ci
dα πe
d RP M
43
= 0 and δ can be taken
0. Since dα
πr
Lemma 4 that if ci >> ce then
then
d post
dα πe
=
(4−3α)(4−α)
18
>
= ce and α > 25 ,
arbitrarily close
to 1, α need not have a monotonic effect on the foreclosure condition in expression (10).44
In other words, if firms value the future highly and if cost differences are large enough
to make the entrant want to claim the entire market post-entry (business stealing), then
more differentiation leads to a lower price being needed to ensure full market capture. In
this instance, differentiation makes exclusion easier because profits post-entry are reduced.
However, if cost differences are small, leading to market segmentation, then differentiation
makes exclusion harder, as competition in the post-entry subgame is softened (competitionsoftening). This increases post-entry profits, making exclusion harder to implement.
43
Note that the incumbent and the entrant are asymmetric here, and the entrant, even if enjoying the
same marginal cost, has an advantage in being more centrally located in terms of preferences. Thus,
there is an effect here that the entrant prefers lower differentiation, as this reduces transport costs for the
(uncontested) consumers to its right.
dπ m
44
For completeness, note that dαac = −2α < 0. Since, in the period of entry, the incumbent enforces the
high monopoly RPM price, and so the key effect is a business-stealing effect whereby the entrant seeks to
undercut the incumbent and can do so more profitably the less differentiated are the products.
29
6.2
Downstream differentiation
In this section, we revert to our baseline case in assuming that the entrant and incumbent
sell goods that are homogeneous from the consumers’ perspective, but allow for differentiation among retailers, again employing the Hotelling framework.
Specifically, we now suppose that there are only two retailers located on a line of length
1. We maintain symmetry between the retailers and allow for greater or lesser substitution
between them by supposing that the retailers are located at a distance β from the half-way
point on the line; one retailer, L, lies to the left (at
(at
1
2
+ β) where 0 ≤ β ≤
1
2.
1
2
− β) and the other, R, to the right
Again, we suppose that transport costs are quadratic so that
a consumer, located at x, gains net utility M − (x − 12 + β)2 − pL from purchasing from the
retailer on the left at price pL and gains M − (x −
1
2
− β)2 − pR from purchasing from the
retailer on the right at price pR . We suppose that M is sufficiently high that the market
is always covered by a monopolist.
As in Section 6.1 and our baseline model, entry is deterred as long as the foreclosure
condition in expression (10) is satisfied. The analysis is slightly more involved in this case,
however, insofar as differentiation among the retailers implies that in the absence of RPM
and, in particular, in a post-entry subgame, retailers would earn positive profits; that is,
πrentry 6= 0. We begin by characterizing properties of πrentry and other relevant profits and
relegate the proofs to the Appendix.
Lemma 5 In the downstream differentiation case when M is sufficiently high that the
market is fully covered, then the entrant’s post-entry profits are independent of the extent of
post
e
downstream differentiation ( dπdβ
in the extent of differentiation
extent of differentiation
m
( dπdβac
= 0); retailers’ post-entry profits are strictly increasing
post
r
( dπdβ
= 1); accommodating profits are decreasing in the
< 0); and the retailers’ profits with only the incumbent and
RP M
RPM can either be increasing or decreasing in the extent of differentiation ( dπrdβ
0 if β >
1
4
and
dπrRP M
dβ
=
1−2β
2
= −β <
> 0 if β < 14 ).
The directions of these comparative statics are intuitive. First, notice that πepost is
independent of β, as differentiation among retailers does not affect the nature of manufacturer competition (where products are undifferentiated). Post-entry profits for retailers
post
r
increase if there is more differentiation ( dπdβ
= 1 > 0); this is for the standard reason that
differentiation softens the intensity of price competition. In considering the profits under
accommodation, loosely speaking, the non-accommodating retailer has a fixed price, and so
30
differentiation does not soften price competition; instead, the entrant and accommodating
retailer prefer little differentiation in the period of accommodation, as the primary effect is
that it is less costly to undercut the other retailer. Finally, profits under RPM, with only
the incumbent active, may be increasing or decreasing in the extent of differentiation—an
integrated monopolist would prefer that β =
1
4
in order to minimize consumer transport
costs, and so either more or less differentiation than this would decrease πrRP M .
Overall, with several effects in play, cases can be found where retailer differentiation
m
makes it easier or harder to exclude an entrant. For δ close to 1, the effect through πac
in Condition (10) is negligible; then, since
dπepost
dβ
= 0, the only effects are through πrRP M
and πrpost . It is easy to verify that the effect through πrpost dominates, and so more retailer
differentiation makes it harder to exclude an entrant. Instead, for lower values of δ, more
differentiation can make it easier to exclude an entrant; for example, this will always be
the case when β <
1
4
and δ is small enough since
m
dπac
dβ
< 0 and
dπrRP M
dβ
> 0 for β < 14 .
Note that earlier studies have shown that product differentiation can have subtle and
ambiguous effects on firms’ ability to collude (see Deneckere (1983), Chang (1991) and
Ross (1992)). We find similar results here where RPM allows duopolist retailers to split
monopoly profits but a retailer can “deviate” by accommodating an entrant, though such
deviation leads to the static Nash outcome of the competitive game (albeit one where the
retailers are supplied by the more efficient entrant rather than by the incumbent). In this
context, our results here are perhaps not surprising but worth highlighting, particularly,
as policy-makers have highlighted the extent of competition as an important factor for
determining whether RPM is likely to be harmful.
7
Policy implications
Antitrust practitioners and academic economists have long debated RPM (the OECD
(2008) roundtable provides a wide-ranging discussion; Matthewson and Winter (1998) and
Winter (2009) provide useful overviews).45 Recognizing that “respected economic analysts
45
Our analysis, in line with much of the literature and policy discussion, is focused on minimum resale
price maintenance. Extending the model to allow for asymmetric downstream firms can allow a role for
maximum resale price maintenance (or price ceilings) in tandem with minimum resale price maintenance
(price floors). For example, consider a downstream segmented market, where in one segment a monopolist
dealer operates and in the other segment dealers are competitive. A price ceiling can overcome the usual
double mark-up problem in the monopolized downstream market creating greater overall industry profits,
while the use of resale price maintenance and wholesale prices allows the incumbent dealer to pass on some
of these profits to the retailers in the competitive segment. However, note that for this channel to operate,
31
. . . conclude that vertical price constraints can have procompetitive effects” (p.1), the
U.S. Supreme Court, in its 2007 Leegin ruling, overturned the 1911 Dr. Miles decision that
viewed RPM as a per se antitrust violation. Similarly, in the E.U., the 2010 Guidelines
on Vertical Restraints allow parties to plead an efficiency defense under Article 101(3) (see
p.63, paragraph 223). These new antitrust regimes, therefore, require antitrust authorities
and other interested parties to trade off the consumer and social benefits of RPM against
the possible harm. To this end, clearly articulated theories of harm are necessary.
It is interesting to note that both Leegin and the E.U. Guidelines on Vertical Restraints
explicitly highlight that “a manufacturer with market power . . . might use resale price
maintenance to give retailers an incentive not to sell the products of smaller rivals or new
entrants” (Leegin p.894) and that “resale price maintenance may be implemented by a
manufacturer with market power to foreclose smaller rivals” (p.64, paragraph 224). In
contrast, most of the economics literature, perhaps due to a reasonable desire to explain
why rule of reason might be more appropriate than per se treatment of RPM, has not
focused on this possible cause of harm (see the literature discussed in Section 2 of this
paper for exceptions). Thus, the absence of a formally-articulated theory has, perhaps, led
to less attention to this cause than is warranted among some policy makers.46
In addition to reinforcing the idea that RPM can be used as a means of upstream
exclusion, in presenting this formally-articulated theory of harm, we provide a counterpoint to some of the screens that have been suggested for determining legitimate uses of
RPM. Policy makers (such as in the OECD (2008) roundtable) and commentators have
suggested that antitrust authorities should distinguish between manufacturer- and retailerinitiated RPM. For example, the Leegin ruling (p.898), citing Posner (2001) states:
It makes all the difference whether minimum retail prices are imposed by the
manufacturers in order to evoke point-of-sale services or by the dealers in order
to obtain monopoly profits.
In this context, it is worth highlighting that in the exclusion theory articulated above, both
the incumbent dealer and retailers stand to gain from RPM, and either side might initiate
the model would also need to be further extended— for example, allowing for the incumbent to operate
with decreasing returns to scale.
46
For example, the OFT’s submission to the OECD roundtable (2008) does not address this cause of
harm in outlining economic theories (pp. 204-207) nor does the United States’ submission in its review of
theories of anti-competitive uses (pp.218-9), and, more generally, there is no mention of exclusion at all in
this 300-page OECD report.
32
RPM for the purpose of exclusion.
Similarly, while the importance of competition (or lack of it) is often stressed, our analysis suggests a nuanced view insofar as imperfect competition through differentiation can
have ambiguous consequences for the possibility of exclusion, though our analysis clearly
relies on some upstream market power. In particular, if the strength of competition between manufacturers (or retailers) is measured using cross-price elasticities, then increased
competition may strengthen (or weaken) the potential for exclusion. Where our theory
is unambiguous is in saying that, all things being equal, adding an extra retailer makes
exclusion harder.
Our analysis highlights a necessary condition for RPM to be used to exclude an entrant
manufacturer: It is critical that the entrant requires an accommodating retailer to compete; if it easy for an entrant to vertically integrate or otherwise deal directly with final
consumers, there is no possibility of exclusion in our model. Similarly, another critical
assumption in the model is that an incumbent manufacturer does not simply disappear
post-entry, leaving the entrant and retailers to share monopoly profits; instead, the industry earns only duopoly profits if entry occurs, so that overall industry profits may be lower
following entry, providing the possibility that the incumbent can use RPM to share surplus
with retailers and foreclose entry.
Lastly, we show that when a monopolist uses RPM, antitrust harm can still emerge.
In particular, in markets where the good sold is undifferentiated (such as—recalling the
American Sugar Refining Company—sugar) and a dominant firm exists, the use of RPM
can be a cause for concern. Existing efficiency-based theories of added service or anticompetitive theories of collusion facilitation have trouble with this setting, as neither fits
the institutional setting.
Unfortunately, the above discussion suggests that many existing screens for the existence of harm deserve cautious application. Should concerns regarding exclusion be raised,
the bound suggested in Section 4.2 might provide a useful first indication of whether the
scope of possible exclusion is large enough to be problematic. This bound can be estimated
by using standard methods (see Ackerberg et al. (2007)). The use of this bound may be
helpful in much the same way that a simple Lerner index is helpful in the evaluation of
market power. If there is little indication that exclusion would be large enough to matter in
an economic sense, then existing screens are likely reasonable. Otherwise, the use of RPM
by a manufacturer with considerable market dominance may warrant further inspection,
where, perhaps, under current screens it would not.
33
8
Conclusion
This paper presents a formal model in which an incumbent manufacturer is able to exclude
a more efficient entrant, by using minimum RPM to increase the profits of retailers in the
event that they refuse to accommodate entry. This makes it prohibitively expensive for
the entrant to enter. We formalize notions of exclusion due to RPM that have repeatedly
surfaced in the economic literature, at least since the 1930s. The recent decision of the
U.S. Supreme Court in Leegin, together with recent policy developments in Europe, has
generated an increased need for theoretical and empirical work on how RPM may harm
competition. This paper explores exclusion as a theory of harm by grounding it in a
theoretical framework. This provides a foundation for further research in the area, both
theoretical and empirical.
It is worth noting that, in our model, we explicitly restrict the use of lump-sum transfers.
Indeed, only the entrant, via R, is able to use lump-sum transfers. In the case of the entrant,
we do this since leaving the contract space unrestricted makes entry easier—if the entrant
were unable to make such payments, then the range of exclusion would be greater (i.e.,
R = 0 by assumption). This makes our finding somewhat more robust. As is the case in
all vertical contracting models, the choice of contract space is a difficult one, more guided
by the application that is being explored than by a deep theory of contracting frictions.
Here, our contracting space has been guided by a wish to understand the possible effects
of minimum RPM.
Nevertheless, little in the model would change if the incumbent made lump-sum transfers rather than shifting surplus via minimum RPM.47 The only difference is that, in the
event one retailer does accommodate entry, the lump-sum transfer to the retailers would
still be paid by the incumbent in the entry period. This makes exclusion slightly harder
and also makes entry expensive for the incumbent. RPM does not have this quality, since
the retailer’s surplus is intrinsically linked to sales. Nonetheless, considering the case of
lump-sum transfers is interesting, since such a contract would look like a period-by-period
slotting fee, which suggests that these fees may also have an exclusionary effect.48 Such
an arrangement is also reminiscent of the exclusive dealing literature (see Simpson and
Wickelgren (2007) and the papers cited therein), in that these papers consider exclusivity
47
The basic contract could be implemented by setting pi = wi = pm
i and using the lump-sum transfer to
shift surplus.
48
Shaffer (1991) also interprets slotting fees as a period-by-period lump-sum transfer.
34
contracts that are induced via lump-sum payments. The framework here suggests that such
agreements may be able to be synthesized implicitly, by utilizing the promise of future rent
transfers if exclusivity continues.49
49
This view is perhaps closest to the contingent contract considered in Simpson and Wickelgren (2007),
where accommodation by one retailer invalidates the exclusivity of the other, thereby reducing the ability
of the accommodating retailer to extract rents due to competition from the others. This leads to an
exclusionary equilibrium. In our setting, the same thing happens, albeit with a lag determined by the
‘length’ of a period (equivalently, the ‘size’ of q(p)).
35
A
Omitted Proofs
Proof of Lemma 3
Proof.
The profit an incumbent could obtain from the incumbent-optimal collusive scheme is
given by the solution to
max (p (q) − ci ) qi ,
q,qi
(11)
subject to the cooperation constraints of the incumbent and the entrant. We proceed by
relaxing the constraint set and considering only the entrant’s cooperation constraint. First
we show that the incumbent-optimal cartel allocation occurs when q lies below q (pm
e ).
Toward a contradiction, we assume that incumbent-optimal cartel allocation occurs
m
when p(q) < pm
e . The cooperation constraint of the entrant when p(q) < pe implies
qi ≤ δq −
δ (ci − ce ) q (ci )
.
p (q) − ce
(12)
Allowing the relaxed version of the above maximization problem to be written as (once
it is observed that the cooperation constraint of the entrant must bind in the incumbentoptimal agreement)
p (q) − ci
(δq (p (q) − ce ) − δ (ci − ce ) q (ci )) ,
p (q) − ce
max
q
(13)
which can be further rewritten as
max
q
π (q) ≡ max
q
πi (q)
(πe (q) − πec ) ,
πe (q)
(14)
where πec is the competitive profit of the entrant (that is, (ci − ce ) q (ci )).
Taking the derivative with respect to q yields
∂π (q)
∂q
=
=
πi0 (q)
πi (q) 0
π 0 (q) πi (q)
c
(πe (q) − πec ) +
πe (q) − e
2 (πe (q) − πe )
πe (q)
πe (q)
(πe (q))
0
c
πi (q)
πi (q) πe 0
(πe (q) − πec ) +
πe (q)
πe (q)
πe (q)2
.
36
(15)
(16)
Evaluating this derivative at any point in the interval [q (pm
e ) , q (ci )] yields
∂π (q) < 0,
∂q q∈[q(ci ),q(pm
e )]
(17)
where we have used the fact that, in this interval, πi0 (q) < 0 and πe0 (q) ≤ 0. Hence, the
optimal level of q lies below q (pm
e ), establishing the contradiction.
As a consequence, the correct constraint to work with is
qi ≤ q −
m
(1 − δ) q (pm
e ) [pe − ce ] + δ (ci − ce ) q (ci )
.
[p (q) − ce ]
(18)
Following the same procedure as above, the incumbent-optimal q is the solution to
max
q
π̃ (q) ≡ max
q
πi (q)
(πe (q) − (1 − δ) πem − δπec )
πe (q)
(19)
and,
π 0 (q)
πi (q) ((1 − δ) πem + δπec ) 0
∂ π̃ (q)
πe (q) ;
= i
(πe (q) − (1 − δ) πem − δπec ) +
∂q
πe (q)
πe (q)2
(20)
further,
∂ π̃ (q) < 0 and
∂q q=q(pm
e )
noting that (18) implies qi = 0 if πe (q) ≤
Hence, the optimal level of q lies in
∂ π̃ (q) > 0,
∂q q∈[0,q(pm )]
(21)
i
δ) πem
(1 −
+ δπec .
m
the interval [q (pm
i ) , q (pe )].
This leads to the
conjecture that the incumbent’s profit is bounded by the profits that accrue from setting
m
p = pm
i and qi equal to that implied by (18) when the inequality binds and q = q (pe ).
To convert this conjecture to a proposition, it must be established that qi is greatest when
m
m
q = q (pm
e ), as compared to any other point in the interval [q (pi ) , q (pe )].
Setting (18) to bind and taking the derivative of qi with respect to q yields
m
∂qi
(1 − δ) q (pm
e ) [pe − ci ] + δ (ci − ce ) q (ci ) ∂p (q)
=1+
.
∂q
∂q
[p (q) − ce ]2
(22)
From the first-order condition of the entrant’s monopoly pricing problem, it must be
37
m
the case that in the interval [q (pm
i ) , q (pe )],
(p (q) − ce )
∂p
≥−
,
∂q
q
(23)
with equality when q = q (pm
e ). Hence, substituting this in yields
m
∂qi
(1 − δ) q (pm
e ) [pe − ci ] + δ (ci − ce ) q (ci )
≥1−
.
∂q
[p (q) − ce ] q
Hence, provided that the numerator is less than the denominator,
sufficient for q =
q (pm
e )
(24)
∂qi
∂q
> 0, which is
to be the largest qi in the relevant range. Note that if the numerator
is greater than the denominator, then, from (18), qi = 0.
Hence, qi is greatest when q = q (pm
e ), as compared to any other point in the interval
m
[q (pm
i ) , q (pe )]. This is sufficient to establish that the incumbent’s profit is bounded from
above by the profits that accrue from setting p = pm
i and qi equal to that implied by
(18) when the inequality binds and q = q (pm
e ). This upper bound on profit is given by
(pm
i −ci )
Collude
m
m
π
= δq (pe ) (pi − ci ) − δ (ci − ce ) q (ci ) (pm
−ce ) .
e
Proof of Lemma 4
Proof. First, consider maximal industry profits in the absence of the entrant. The asM = M − 1 and that π RP M =
sumption of full market coverage implies that pRP
r
i
M −1−ci
.
n
Note that the optimal price in the absence of full market coverage would maximize
√
(p − ci ) M − p; the solution is p = 2M3+ci , and so the full market coverage assumption is
equivalent to
2M +ci
3
Next, consider
< M − 1 or, equivalently, M > 3 + ci .
m.
πac
Given that the rival retailers set their price at M − 1, the entrant
and accommodating retailer would agree on a retail price of M − 1 − α2 and cover the
market. Trivially, this is the optimal strategy since if the higher-cost (and less centrally
located) incumbent would cover the market, it is more attractive only for the entrant to
do so. Formally, if the entrant charged a price p and was not covering the market, then
the consumer indifferent between the incumbent and entrant would be at distance x from
the entrant where M − (M − 1) − (α − x)2 = M − p − x2 ; it follows that the entrant would
(M −1−p+α2 )
choose a price to maximize (p − ce )(
+ 1 − α), which yields a maximized value
2α
2 −1 2
M
+2α−c
−α
(
)
e
equal to 18
, where this expression is valid as long as the consumer that is
α
indifferent between the incumbent’s and the entrant’s goods is interior; this requires that
(M −1− 21 M +α+ 12 ce − 21 α2 − 12 +α2 )
< α or M < 3 − ce − α(2 − 3α), but this is inconsistent with
2α
38
the earlier restriction that M > 3 + ci . It follows that the entrant and accommodating
m = M − 1 − α2 − c .
retailer would charge a price M − 1 − α2 and cover the market and πac
e
Finally, we turn to consider πepost . Note that Bertrand competition among retailers
ensures a retail price of we for the entrant’s product and wi for the incumbent’s product. We
solve for the Nash equilibrium of the wholesale pricing game. Suppose that the incumbent
chooses wi and the entrant we ≤ wi .50 Although we assume full market coverage, there
remain two cases to consider:51
(i) The entrant serves the whole market. In this case, the incumbent would charge a
price equal to ci , and the entrant would charge pe = ci − α2 and earn profits of πepost =
ci − ce − α2 ; or
(ii) both the entrant and the incumbent are active.
In this latter case, the incumbent charges wi , and the entrant charges we , and here
the indifferent consumer is x such that M − wi − x2 = M − we − (α − x)2 , and so x =
(we −wi +α2 )
(we −wi +α2 )
.
It
follows
that
the
incumbent
chooses
w
to
maximize
(w
−
c
)
.
i
i
i
2α
2α
Since an incumbent monopolist would fully cover the market, it follows that the entrant,
whose equilibrium price can later be easily verified to be below M − 1, will sell to all
consumers that are located at any y ≥ α, and so the demand for the entrant is given by
(wi −we +α2 )
(wi −we +α2 )
(
+1−α). Therefore, the entrant chooses we to maximize (we −ce )(
+
2α
2α
1 − α).
The first-order conditions for the incumbent and entrant yield best-response functions
wiBR (we ) = 21 we + 12 ci + 21 α2 and weBR (wi ) = α+ 12 ce + 21 wi − 12 α2 . We can solve for equilibrium
by solving for the intersection of these best-response functions; this is at we =
and wi =
2α+ce +2ci +α2
.
3
„
Note that this solution requires that x ∈ (0, α) that is
1 2α+ce −ci +α2
∈ (0, α) or
6
α
2 2
4α−c
(
e +ci −α )
post
1
πe = 18
α
4α+2ce +ci −α2
3
4α+2ce +ci −α2
2α+ce +2ci +α2
−
+α2
3
3
«
2α
=
equivalently α(2 + α) > ci − ce > α(2 − 5α). Under this solution,
by substituting for we and wi in the entrant’s profits function.
Proof of Lemma 5 The proof of this Lemma requires the following lemma (Lemma 6);
the rest of the proof is contained after the proof of Lemma 6.
50
It is clear that this inequality will hold in equilibrium and can be easily verified after solving for
equilibrium values.
51
We continue to ignore equilibria in which the incumbent prices below cost, yet gets no demand.
39
Lemma 6 In the downstream differentiation
case when M is sufficiently)high that the mar(
1
2
if β ≥ 14
2 (M − β − ci )
ket is fully covered, then πrRP M =
, πepost = ci − ce ,
1
1
1
2
if β < 4
2 (M − ( 2 − β) − ci )

(M +β(2−β)−ce )2
1
1

if β ≥ 4 and β 2 + 6β + ce > M

16
β


 M − β(2 + β) − c
if β ≥ 14 and β 2 + 6β + ce < M
e
post
m
πr = β, and πac =
2
1 (4M +β(12−4β)−4ce −1)

if β < 14 and 1 + β(20 + 4β) + 4ce > 4M


256
β


M − ( 12 − β)2 − 2β − ce if β < 14 and 1 + β(20 + 4β) + 4ce < 4M






.





Proof. First, consider maximal industry profits in the absence of the entrant. Note that
since retailers are located at
1
2
− β and
1
2
+ β on the Hotelling line, a consumer need only
max{ 21
travel a maximal
− β, β};
( distance of
)the assumption of full
( market coverage implies
1
1
2
2
M −β
if β ≥ 4
if β ≥
RP M =
M =
2 (M − β − ci )
and
that
π
that pRP
r
i
1
1
1
1
2
2
M − ( 2 − β)
if β < 4
if β <
2 (M − ( 2 − β) − ci )
Next, turning to the post-entry game, Bertrand competition among manufacturers
with ce sufficiently close to ci , such that the entrant’s monopoly price is above ci , results
in wi = we = ci and the entrant making all sales. The full market coverage assumption,
therefore, yields πepost = ci − ce .
Let us now consider retailers’ post-entry period profits: Retailers set prices pL and pR
while incurring a wholesale cost of ci for the good. Suppose, as can be verified is the case
in equilibrium, that the indifferent consumer will be in between the two retailers; then,
the indifferent consumer will be at a distance x from the left retailer where M − pL −
x2 = M − pR − (2β − x)2 , so x =
+4β 2
pR −pL
1
2 −β +
4β
pR −pL +4β 2
,
4β
the demand for the left retailers is simply
2
L +4β
, and the demand for the right retailer is given by 12 −β +2β − pR −p4β
.
The left retailer maximizes profits by choosing pL to maximize (pL − ci )( 12 − β +
pR −pL +4β 2
).
4β
The first-order condition yields pL = β + 12 ci + 12 pR ; and since the prob-
post
=
lem of the right retailer is symmetric, in equilibrium, pL = pR = ci + 2β and πR
1
2 (ci
+ 2β − ci ) = β.
m . Without loss of generality, suppose that it is the left
It remains to characterize πac
retailer who accommodates the entrant. The right retailer, as above, has a price of M − β 2
if β ≥
1
4
and a price of M − ( 12 − β)2 if β < 14 . In each case, there are two possibilities.
Note that, as above, the consumer that is indifferent between the left and right retailer is
at a distance
pR −pL +4β 2
4β
as long as this takes a value in the range [0, 12 + β]. In this case,
m = max (p − c )( 1 − β +
therefore, πac
p
e 2
β+
ce +pR
2
pR −p+4β 2
)
4β
2
=
1 (2β−ce +pR )
16
β
with associated price
and, otherwise, the retailer sells to all the market and so will make the right40
1
4
1
4
)
.
most consumer indifferent; i.e., he will set p such that M − p − (β + 12 )2 = M − pR − (β − 21 )2
so that p = pR − 2β.
2
Summarizing, in case β ≥ 41 , when
and if
β <
c +pR
)+4β 2
2
M −β 2 −(β+ e
4β
1
4,
and if
then when
>
1
2
2
m =
< 12 +β, πac
2
1 (2β−ce +M −β )
16
β
m = p − 2β − c . In the alternative case where
+ β, then πac
e
R
M −( 12 −β)2 −(β+
M −( 12 −β)2 −(β+
−β
)+4β 2
M −β 2 −(β+ ce +M
2
4β
1 −β)2
ce +M −( 2
)+4β 2
2
4β
1 −β)2
ce +M −( 2
)+4β 2
2
4β
expressions yields the expression for
>
aq
πm
1
2
<
1
2
m =
+ β, πac
1
2 2
1 (2β−ce +M −( 2 −β)
16
β
)
m = p − 2β − c . Simplifying these
+ β then πac
e
R
in the statement of the lemma.
Proof of Lemma 5
Proof. These results are immediate from Lemma 6, though it is perhaps worth noting that
m
m
e
1
M − 2β − ce + 3β 2 M +β(2−β)−c
<
the comparative statics of dπdβac are given by dπdβac = − 16
β2
m
dπac
1
2
dβ = −2(1 + β) < 0 if β ≥ 4 and β + 6β + ce < M ,
m
dπac
4M +12β−4ce −4β 2 −1
1
2
< 0 if β < 41 and 1 + β(20 +
dβ = − 256 4M − 12β − 4ce + 12β − 1
β2
m
4β) + 4ce > 4M , and dπdβac = −1 − 2β < 0 if β < 14 and 1 + β(20 + 4β) + 4ce < 4M .
0 if β ≥
1
4
and β 2 + 6β + ce > M ,
The inequalities can be shown by recalling that the full market coverage assumption—
M > 3 + ci —is maintained throughout.
References
[1] Abito, Jose Miguel and Julian Wright (2008), Exclusive Dealing with Imperfect Downstream Competition, International Journal of Industrial Organization, 26(1), 227–246.
[2] Ackerberg, Daniel, C. Lanier Benkard, Steven Berry and Ariel Pakes (2007), Econometric Tools for Analyzing Market Outcomes, Ch. 63 in Handbook of Econometrics,
Volume 6A, James Heckman and Edward Leamer (eds.), North-Holland, Amsterdam.
[3] Argenton, Cédric (2010), Exclusive Quality, Journal of Industrial Economics, 58(3),
690-716.
[4] Bowman, Ward (1955), The Prerequisites and Effects of Resale Price Maintenance,
The University of Chicago Law Review, 22(4), 825-873.
[5] Brennan, Timothy (2008), RPM as exclusion: Did the US Supreme Court stumble
upon the missing theory of harm?, The Antitrust Bulletin, 53(4), 967-986.
41
[6] Cassady, Ralph (1939), Maintenance of Resale Prices by Manufacturers, Quarterly
Journal of Economics, 53(3), 454-464.
[7] Chang, M. (1991), The effects of product differentiation on collusive pricing, International Journal of Industrial Organization, 9(3), 453-469.
[8] Chen, Zhijun and Greg Shaffer (2009), Naked Exclusion with Minimum-Share Requirements, working paper, Simon School of Business, University of Rochester.
[9] Comanor, William and Patrick Rey (2000), Vertical Restraints and the Market Power
of Large Distributors, Review of Industrial Organization, 17, 135-153.
[10] Deneckere, R. (1983) “Duopoly supergames with product differentiation,” Economics
Letters 11, 37-42.
[11] Deneckere, Raymond, Howard Marvel and James Peck (1996), Demand Uncertainty,
Inventories, and Resale Price Maintenance, Quarterly Journal of Economics, 111(3),
885-914.
[12] Deneckere, Raymond, Howard Marvel and James Peck (1997), Demand Uncertainty
and Price Maintenance: Markdowns as Destructive Competition, American Economic
Review, 87(4), 619-641.
[13] Eichner, Alfred (1969), The Emergence of Oligopoly.
[14] Elzinga, Kenneth and David Mills (2008), The Economics of Resale Price Maintenance,
in Issues in Competition Law and Policy, ABA Section of Antitrust Law, 1841.
[15] Fumigalli, Chiara and Massimo Motta (2006), Exclusive Dealing and Entry, when
Buyers Compete, American Economic Review, 96(3), 785-795.
[16] Gammelgaard, Soren (1958), Resale Price Maintenance, Project No. 238, European
Productivity Agency, Organisation for European Economic Cooperation, Paris.
[17] Gilligan, Thomas W. (1986), The Competitive Effects of Resale Price Maintenance,
RAND Journal of Economics, 17(4), 544-556.
[18] Harrington, Joseph E. Jr (1991), The Determination of Price and Output Quotas in
a Heterogenous Cartel, International Economic Review, 32(4), 767-792.
42
[19] Hersch, Phillip L. (1994), The Effects of Resale Price Maintenance on Shareholder
Wealth: The Consequences of Schwegmann, Journal of Industrial Economics, 42(2),
205-216.
[20] Ippolito, Pauline (1991), Resale Price Maintenance: Empirical Evidence from Litigation, Journal of Law and Economics, 34(2), 263-294.
[21] Ippolito, Pauline and Thomas R. Overstreet (1996), Resale Price Maintenance: An
Economic Assessment of the Federal Trade Commission’s Case against Corning Glass
Works, Journal of Law and Economics, 39(1), 285-328.
[22] Jullien, Bruno and Patrick Rey (2007), Resale Price Maintenance and Collusion,
RAND Journal of Economics, 38(4), 983-1001.
[23] Klein, Benjamin and Kevin Murphy (1988), Vertical Restraints as Contract Enforcement Mechanisms, Journal of Law and Economics, 31(2), 265-297.
[24] Mailath, George and Larry Samuelson (2006), Repeated Games and Reputations: Long
Run Relationships, Oxford University Press, Oxford.
[25] Marvel, Howard (1994), The Resale Price Maintenance Controversy: Beyond the Conventional Wisdom, Antitrust Law Journal, 63(1), 59-92.
[26] Marvel, Howard and Stephen McCafferty, (1984), Resale Price Maintenance and Quality Certification, Rand Journal of Economics, 15(3), 346-59.
[27] Marvel, Howard and Stephen McCafferty (1985), The Welfare Effects of Resale Price
Maintenance, Journal of Law and Economics, 28, 363-79.
[28] Marx, Leslie and Greg Shaffer (2004), Rent Shifting, Exclusion, and Market-Share
Discounts, Working Paper.
[29] Miklos-Thal, Jeanine (2010) Optimal Collusion under Cost Asymmetry, Economic
Theory, forthcoming; online version at http://dx.doi.org/10.1007/s00199-009-0502-9
[30] OECD (2008) Policy Rountables: Resale Price Maintenance.
[31] Matthewson, Frank and Ralph Winter (1998) The Law and Economics of Resale Price
Maintenance, Review of Industrial Organization, 13, pp. 57-84.
43
[32] Ordover, Janusz A., Garth Saloner and Steven C. Salop (1988), Equilibrium Vertical
Foreclosure, American Economic Review, 80, pp. 127-42.
[33] Ornstein, Stanley and Dominique M. Hassens (1987), Resale Price Maintenance: Output Increasing or Restricting? The Case of Distilled Spirits in the United States,
Journal of Industrial Economics, 36(1), 1-18.
[34] Overstreet, Thomas R. (1983), Resale Price Maintenance: Economic Theories and
Empirical Evidence, Bureau of Economics Staff Report to the Federal Trade Commission.
[35] Posner, Richard A. (2001) Antitrust Law: 2nd Edition University of Chicago Press.
[36] Rasmusen, Eric, Mark Ramseyer and John Wiley (1991), Naked Exclusion, American
Economic Review, 81(5), 1137-1145.
[37] Rey, Patrick and Thibaud Vergé (2004), Bilateral Control with Vertical Restraints,
RAND Journal of Economics, 35(4), 728-746.
[38] Rey, Patrick and Thibaud Vergé (2009), Resale Price Maintenance and Interlocking
Relationships, Journal of Industrial Economics, forthcoming.
[39] Rey, Patrick and Thibaud Vergé (2008), “Economics of Veritical Restraints”, Ch. 9 in
Handbook of Antitrust Economics, Paolo Buccirossi (ed.), MIT Press, Boston.
[40] Rey, Patrick and Jean Tirole (2007), “A Primer on Foreclosure”, Ch. 33 in Handbook
of Industrial Economics, Volume 3, Mark Armstrong and Rob Porter (eds), North
Holland, Amsterdam.
[41] de Roos, Nicolas (2006), Examining models of collusion: The market for lysine, International Journal of Industrial Organization, 24(6), 1083-1107.
[42] Ross, Tom (1992), Cartel Stability and Product Differentiation, International Journal
of Industrial Organization, 10(1), 1-13.
[43] Segal, Ilya and Michael Whinston (2000), Naked Exclusion: Comment, American
Economic Review, 90(1), 296-309.
[44] Shaffer, Greg (1991), Slotting Allowances and Resale Price Maintenance: A Comparison of Facilitating Practices, RAND Journal of Economics, 22(1), 120-135.
44
[45] Simpson, John and Abraham Wickelgren (2007), Naked Exclusion, Efficient Breach
and Downstream Competition, American Economic Review, 97(4), 1305-1320.
[46] Telser, Lester (1960), Why Should Manufacturers Want Fair Trade?, Journal of Law
and Economics, 3, 86-105.
[47] Tirole, Jean (1988), The Theory of Industrial Organization, MIT Press, Cambridge.
[48] Whinston, Michael D. (2006), Lectures on Antitrust Economics, MIT Press, Cambridge.
[49] Winter, Ralph A. (2009), Presidential Address: Antitrust restrictions on single-firm
strategies, Canadian Journal of Economics, 42, pp. 1207-1239.
[50] Yamey, Basil (1954), The Economics of Resale Price Maintenance, Sir Isaac Pitman
& Sons, Ltd., London.
[51] Yamey, Basil (1966), Introduction: The Main Economic Issues, Ch.1 in Resale Price
Maintenance: A Comparative American-European Perspective, Basil Yamey (Ed.),
AdlineTransaction, Chicago.
[52] Zerbe, Richard (1969), The American Sugar Refinery Company, 1887-1914: The Story
of a Monopoly, Journal of Law and Economics, 12(2), 339-375.
45